Least Common Multiple (LCM) of 99 and 58
The least common multiple (LCM) of 99 and 58 is 5742.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 99 and 58?
First, calculate the GCD of 99 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 58 = 1 remainder 41 |
| 2 | 58 ÷ 41 = 1 remainder 17 |
| 3 | 41 ÷ 17 = 2 remainder 7 |
| 4 | 17 ÷ 7 = 2 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 117 | 7839 |
| 62 and 40 | 1240 |
| 112 and 195 | 21840 |
| 42 and 114 | 798 |
| 33 and 190 | 6270 |